For digital transmission systems, in particular optical transmission systems, transmission is sensitive to noise. Differential decoding is used to reduce error bursts induced by phase slips. Soft differential (SD) decoding proves excellent tolerance against non-linear phase noise. Differential decoding, however, introduces a Bit Error Rate (BER) penalty in the B2B (Back-to-Back) transmission between a transmitting device and a receiving device. In the case of soft differential decoding, two consecutive values are multiplied before a decision is made. Thus, the total noise power is doubled, which translates into an (optical) signal-to-noise ratio degradation. To mitigate the differential decoding penalty, multi-symbol phase estimation (MSPE) methods are known. These methods, however, suffer from complex implementation. Alternatively, non-redundant error correction (NEC) is known as the classical scheme to mitigate the differential penalty. Non-redundant error correction, however, may deliver poor performance.
Differential encoding approximately doubles the error rate compared to ordinary M-PSK but this may be overcome by only a small increase in signal to noise ratio Eb/N0. As there will be a physical channel between the transmitter and receiver in the communication system, this channel will, in general, introduce an unknown phase-shift to the PSI: signal. In these cases, the differential schemes can yield a better error-rate than the ordinary schemes which rely on precise phase information. For a signal that has been differentially encoded, there is an alternative method of demodulation. Instead of demodulating as usual and ignoring carrier-phase ambiguity, a phase between two successive received symbols is compared and used to detect the transmitted data. When differential encoding is used in this manner, the scheme is known as differential phase-shift keying (DPSK) or differential quadrature phase-shift keying (DQPSK).